Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional)

Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional)

1.05 Radiation-Induced Effects on Material Properties of Ceramics (Mechanical and Dimensional) K E Sickafus University of Tennessee, Knoxville, TN, USA ß 2012 Elsevier Ltd All rights reserved 1.05.1 1.05.2 1.05.2.1 1.05.2.2 1.05.2.3 1.05.2.3.1 1.05.2.3.2 1.05.2.3.3 1.05.2.3.4 1.05.2.3.5 1.05.2.3.6 1.05.2.3.7 1.05.2.3.8 1.05.2.3.9 1.05.2.3.10 1.05.2.3.11 1.05.2.4 1.05.3 1.05.3.1 1.05.3.2 1.05.3.3 1.05.3.4 1.05.4 References Introduction Radiation Effects in Ceramics: A Case Study – a-Alumina Versus Spinel Introduction to Radiation Damage in Alumina and Spinel Point Defect Evolution and Vacancy Supersaturation Dislocation Loop Formation in Spinel and Alumina Introduction to atomic layer stacking Charge on interstitial dislocations Lattice registry and stacking faults I: (0001) Al2O3 Lattice registry and stacking faults II: {111} MgAl2O4 Lattice registry and stacking faults III: {1010} Al2O3 Lattice registry and stacking faults IV: {110} MgAl2O4 Unfaulting of faulted Frank loops I: (0001) Al2O3 Unfaulting of faulted Frank loops II: {111} MgAl2O4 Unfaulting of faulted Frank loops III: {1010} Al2O3 Unfaulting of faulted Frank loops IV: {110} MgAl2O4 Unfaulting of faulted Frank loops V: experimental observations Amorphization in Spinel and Alumina Radiation Effects in Other Ceramics for Nuclear Applications Radiation Effects in Uranium Dioxide Radiation Effects in Silicon Carbide Radiation Effects in Graphite Radiation Effects in Other Ceramics Summary Abbreviations dpa BF TEM i v ccp hcp SHI PKA CVD Displacements per atom Bright-field Transmission electron microscopy Interstitial Vacancy Cubic close-packed Hexagonal close-packed Swift heavy ion Primary knock-on atom Chemical vapor deposition 1.05.1 Introduction Ceramic materials are generally characterized by high melting temperatures and high hardness values Ceramics are typically much less malleable than 123 124 124 125 127 127 127 129 129 130 130 131 132 132 133 133 134 136 136 136 137 138 138 139 metals and not as electrically or thermally conductive Nevertheless, ceramics are important materials in fission reactors, namely, as constituents in nuclear fuels, and are widely regarded as candidate materials for fusion reactor applications, particularly as electrical insulators in plasma diagnostic systems These applications call for highly robust ceramics, materials that can withstand high radiation doses, often under very high-temperature conditions Not many ceramics satisfy these requirements One of the purposes of this chapter is to examine the fundamental mechanisms that lead to the relative radiation tolerance of a select few ceramic compounds, versus the susceptibility to radiation damage exhibited by most other ceramics Ceramics are, by definition, crystalline solids The atomic structures of ceramics are often highly complex compared with those of metals As a consequence, we lack a detailed understanding of atomic 123 124 Radiation-Induced Effects on Material Properties of Ceramics processes in ceramics exposed to radiation Nevertheless, progress has been made in recent decades in understanding some of the differences between radiation damage evolution in certain ceramic compounds In this chapter, we examine the radiation damage response of a select few ceramic compounds that have potential for engineering applications in nuclear reactors We begin by comparing and contrasting the radiation damage response of two particular (model) ceramics: a-alumina (Al2O3, also known as corundum in polycrystalline form, or ruby or sapphire in single crystal form) and magnesioaluminate spinel (MgAl2O4) Under neutron irradiation, alumina is highly susceptible to deleterious microstructural evolution, which ultimately leads to catastrophic swelling of the material On the other hand, spinel is very resistant to the microscopic phenomena (particularly nucleation and growth of voids) that lead to swelling under neutron irradiation We consider the atomic and microstructural mechanisms identified that help to explain the marked difference in the radiation damage response of these two important ceramic materials The fundamental properties of point defects and radiation-induced defects are discussed in Chapter 1.02, Fundamental Point Defect Properties in Ceramics, and the effects of radiation on the electrical properties of ceramics are presented in Chapter 4.22, Radiation Effects on the Physical Properties of Dielectric Insulators for Fusion Reactors It is important to be cognizant of the irradiation conditions used to produce a particular radiation damage response Microstructural evolution can vary dramatically in a single compound, depending on the following irradiation parameters: (1) irradiation source–irradiation species and energies – these give rise to the so-called ‘spectrum effects,’ (2) irradiation temperature, (3) irradiation particle flux, and (4) irradiation elapsed time and particle fluence Throughout this chapter, we pay particular attention to the variations in radiation damage effects due to differences in irradiation parameters A single ceramic material can exhibit radiation tolerance under one set of irradiation conditions, while alternatively exhibiting damage susceptibility under another set of conditions A good example of this is MgAl2O4 spinel Spinel is highly radiation tolerant in a neutron irradiation environment but very susceptible to radiation-induced swelling when exposed to swift heavy ion (SHI) irradiation Finally, it is important to note that radiation tolerance refers to two distinctly different criteria: (1) resistance to a crystal-to-amorphous phase transformation; and (2) resistance to dislocation and void nucleation and growth Both of these phenomena lead (usually) to macroscopic swelling of the material, but the causes of the swelling are completely different The irradiation damage conditions that produce these two materials’ responses are also typically very different We examine these two radiation tolerance criteria through the course of this chapter 1.05.2 Radiation Effects in Ceramics: A Case Study – a-Alumina Versus Spinel 1.05.2.1 Introduction to Radiation Damage in Alumina and Spinel a-Al2O3 and MgAl2O4 are two of the most important engineering ceramics They are both highly refractory oxides and are used as dielectrics in electrical applications (capacitors, etc.) Both a-Al2O3 and MgAl2O4 have been proposed as potential insulating and optical ceramics for application in fusion reactors.1–3 In a magnetically confined fusion device, these applications include (1) insulators for lightly shielded magnetic coils; (2) windows for radiofrequency heating systems; (3) ceramics for structural applications; (4) insulators for neutral beam injectors; (5) current breaks; and (6) direct converter insulators.3 Such devices in a fusion reactor environment will experience extreme environmental conditions, including intense radiation fields, high heat fluxes and heat gradients, and high mechanical and electrical stresses A special concern is that under these extreme environments, ceramics such as a-Al2O3 and MgAl2O4 must be mechanically stable and resistant to swelling and concomitant microcracking Over the last 30 years, many radiation damage experiments have been performed on a-Al2O3 and MgAl2O4 under high-temperature conditions by a number of different research teams Figure shows the results of one such study, where the high temperature, neutron irradiation damage responses of a-Al2O3 and MgAl2O4 are compared The plot in Figure was adapted from Figure in an article by Kinoshita and Zinkle,4 based on experimental data obtained by Clinard et al and Garner et al.5–8 The neutron (n) fluence on the lower abscissa in Figure refers to fission or fast neutrons, that is, neutrons with energies greater than $0.1 MeV Figure also shows the equivalent displacement damage dose on the upper abscissa, in units of Radiation-Induced Effects on Material Properties of Ceramics Swelling (%) Displacements per atom (dpa) 10 100 1000 a-Al2O3 1100 k 1025 k 925 k MgAl2O4 658–1100 K -1 1025 1026 1027 Neutron fluence (n m-2) 1028 Figure Volume swelling versus neutron fluence in a-Al2O3 alumina and MgAl2O4 spinel displacements per atom (dpa) These dpa estimates are based on the approximate equivalence (for ceramics) of dpa per 1025 n mÀ2 (En > 0.1 MeV).9 Figure shows a stark contrast between the radiation damage behavior, particularly the volume swelling behavior, between a-Al2O3 and MgAl2O4 Specifically, MgAl2O4 spinel exhibits no swelling in the temperature range 658–1100 K, for neutron fluences ranging from $3  1026 to 2.5  1027 n mÀ2 (3–200 dpa) On the contrary, a-Al2O3 irradiated at temperatures between 925–1100 K exhibits significant volume swelling, ranging from $1 to 5% over a fluence range of  1025 to  1026 n mÀ2 (1–30 dpa) The purpose of the following discussion is to reveal the reasons for the tremendous disparity in radiation-induced volume swelling between alumina and spinel Figure shows a bright-field (BF) transmission electron microscopy (TEM) image that reveals the microstructure of a-Al2O3 following fast neutron irradiation at T ¼ 1050 K to a fluence of  1025 n mÀ2 c 100 nm Figure Bright-field transmission electron microscopy image of voids formed in a-Al2O3 irradiated at 1050 K to a fluence of  1025 n mÀ2 ($3 dpa) (micrograph courtesy of Frank Clinard, Los Alamos National Laboratory) 125 ($3 dpa) The micrograph reveals a high density of small voids (2–10 nm diameter), arranged in rows along the c-axis of the hexagonal unit cell for the a-Al2O3 When voids are arrayed in special crystallographic arrangements, as in Figure 2, the overall structure is referred to as a void lattice Figure shows the underlying explanation for the pronounced volume swelling of a-Al2O3 shown in Figure 1, namely the formation of a void lattice with increasing neutron radiation dose This phenomenon is well known in many irradiated materials, both metals and ceramics, and is referred to as void swelling Susceptibility to void swelling is a very undesirable material trait and basically disqualifies such a material from use in extreme environments (in this case, high temperature and high neutron radiation fields) It should be noted that TEM micrographs (not shown here) obtained from MgAl2O4 spinel irradiated under similar conditions to those in Figure show no evidence of voids of any size 1.05.2.2 Point Defect Evolution and Vacancy Supersaturation Voids are a consequence of a supersaturation of vacancies in the lattice and the tendency of excess vacancies to condense into higher-order defect complexes (either vacancy loops or voids) However, the root cause of void formation is actually not the vacancies, but the interstitials Each atomic displacement event during irradiation produces a pair of defects known as a Frenkel pair The constituents of a Frenkel pair are an interstitial (i) and a vacancy (v) Interstitials are more mobile than vacancies at most temperatures (at low-to-moderate temperatures, say less than half the melting point (0.5Tm), vacancies are essentially immobile in most materials), such that i-defects freely migrate around the lattice, while v-defects either remain stationary or move much smaller distances than i-defects Because i-defects are highly mobile, they are able to diffuse to other lattice imperfections, such as dislocations, grain boundaries, and free surfaces, where they often are readily absorbed This situation leads to a supersaturation of vacancies, that is, a condition in which the bulk vacancy concentration exceeds the complementary bulk interstitial concentration This is a highly undesirable circumstance for a material exposed to displacive radiation damage conditions, because the v-defect concentration will continue to grow (unchecked) at approximately the Frenkel defect production rate, while the i-defect concentration 126 Radiation-Induced Effects on Material Properties of Ceramics will reach a steady-state concentration, determined by interstitial mobility and by the concentration of extended defects (extended defects presumably serve as sinks for interstitial absorption) The v-defect concentration will inevitably reach a critical stage at which the lattice can no longer support the excessive concentration of vacancies, at which point the v-defects will migrate locally and condense to form voids (or vacancy loops or clusters) This entire process, initiated by the supersaturation of vacancies, causes the material to undergo macroscopic swelling, and the material becomes susceptible to microcracking or failure by other mechanical mechanisms This, indeed, is the fate suffered by a-Al2O3 when exposed to a neutron (displacive) radiation environment It is interesting that a supersaturation of vacancies can even be established in a material devoid of extended defects, such as a high-quality single crystal or a very large-grained polycrystalline material Single crystal a-Al2O3 (sapphire) is an example of just such a material.6 When freely migrating i-defects are unable to readily ‘find’ lattice imperfections such as grain boundaries and dislocations, they instead ‘find’ one another Interstitials can bind to form diinterstitials or higher-order aggregates Eventually, a new extended defect, produced by the condensation of i-defects, becomes distinguishable as an interstitial dislocation loop (also known as an interstitial Frank loop) Once formed, such a lattice defect acts as a sink for the absorption of additional freely migrating i-defects With this, the conditions for a supersaturation of vacancies and macroscopic swelling are established The defect situation just described can be conveniently summarized using chemical rate equations as described in detail in Chapter 1.13, Radiation Damage Theory In eqn [1], we employ a simplified pair of rate equations to show the time-dependent fate of interstitials and vacancies produced under irradiation for an imaginary single crystal of A atoms: dCi t ị dt ẳ Pi AA ! Ai ỵ VA ị Riv Ai ỵ VA ! AA ị ẵ1a N ðnucleation rate for interstitial loopsÞ ÀGðgrowth rate for interstitial loopsÞ dCv t ị dt ẳ Pv Riv AA ! Ai ỵ VA ị Ai ỵ VA ! AA ị ẵ1b where Ci(t) and Cv(t) are the time-dependent concentrations of interstitials and vacancies, respectively; Pi and Pv are the production rates of interstitials and vacancies, respectively (equal to the Frenkel pair production rate); Ri–v is the recombination rate of interstitials and vacancies (i.e., the annihilation rate of i and v point defects when they encounter one another in the matrix); N and G are the nucleation and growth rates, respectively, of interstitial loops; AA is an A atom on an A lattice site; Ai is an interstitial A atom; and VA is a vacant A lattice site (an A vacancy) (This equation for vacancies assumes low or moderate temperatures, such that vacancies are effectively immobile Under high-temperature irradiation conditions, we would need to add nucleation and growth terms for voids, vacancy loops, or vacancy clusters Reactions with preexisting defects are also ignored in eqn [1].) Note in eqn [1] that i–v recombination, Ri–v, is a harmless point defect annihilation mechanism (it restores, locally, the perfect crystal lattice) On the contrary, nucleation and growth (N and G) of interstitial loops are harmful point defect annihilation mechanisms, in the sense that these mechanisms leave behind unpaired vacancies in the lattice, thus establishing a supersaturation of vacancies, which is a necessary condition for swelling It is interesting to compare and contrast the neutron radiation damage behavior shown in Figure of alumina (a-Al2O3) and spinel (MgAl2O4) single crystals, in terms of the defect evolution described in eqn [1] Alumina must be described as a highly radiation-susceptible material, due to its tendency to succumb to radiation-induced swelling Spinel, on the other hand, is to be considered a radiationtolerant material, in view of its ability to resist radiation-induced swelling According to eqn [1], we can speculate that mechanistically, nucleation and growth of interstitial dislocation loops are much more pronounced in alumina than in spinel Also, eqn [1] suggests that harmless i–v recombination must be the most pronounced point defect annihilation mechanism in spinel so that a supersaturation of vacancies and concomitant swelling is avoided Indeed, it turns out that nucleation and growth of dislocation loops are far more pronounced in alumina than in spinel, as discussed in detail next The dislocation loop story described below is rich with the complexities of dislocation crystallography and dynamics The unraveling of the mysteries of dislocation loop evolution in alumina versus spinel should be considered one of the greatest achievements ever in the field of radiation effects in ceramics, even though this was accomplished some 30 years ago! This story also illustrates the tremendous complexity of radiation damage behavior in ceramic materials, wherein point defects are created on both anion and cation sublattices, and where the defects generated often assume significant Coulombic charge states in Radiation-Induced Effects on Material Properties of Ceramics highly insulating ceramics (alumina and spinel are large band gap insulators) The earliest stages of the nucleation and growth of interstitial dislocation loops are currently impossible to interrogate experimentally TEM has been used as a very effective technique for examining the structural evolution of dislocation in irradiated solids but only after the defect clusters have grown to diameters of about nm Interestingly, important changes in dislocation character probably occur in the early stages of dislocation loop growth, when loop diameters are only between and 50 nm.10 Therefore, we must speculate about the nature of nascent dislocation loops produced under irradiation damage conditions 1.05.2.3 Dislocation Loop Formation in Spinel and Alumina 1.05.2.3.1 Introduction to atomic layer stacking Results of numerous neutron and electron irradiation damage studies suggest that two types of interstitial dislocation loops nucleate in a-Al2O3: (1) 1/3 [0001] (0001); and (2) 1=3h1011if1010g (see, e.g., the review by Kinoshita and Zinkle4) The first of these involves precipitation on basal planes in the hexagonal a-Al2O3 structure, while the second is due to precipitation on m-type prism planes In MgAl2O4, similar studies indicate that primitive interstitial dislocation loops also have two characters: (1) 1/6 h111i {111} and (2) 1/4 h110i {110}.4 Though the crystal structure of spinel is cubic, compared with that of alumina, which is hexagonal, the nature of the dislocation loops formed in spinel is similar to those in alumina: {111} spinel loops are analogous to (0001) alumina loops; likewise, {110} spinel loops are analogous to f1010g alumina loops We will first compare and contrast {111} spinel versus (0001) alumina loops and later discuss {110} spinel versus f1010g alumina loops Both spinel h111i {111} and alumina [0001] (0001) interstitial dislocation loops involve insertion of extra atomic layers perpendicular to the h111i and [0001] directions, respectively These layers are either pure cation or pure anion layers In both spinel and alumina, anion layers along h111i and [0001] directions, respectively (i.e., along the direction in both structures), are close packed (specifically, they are fully dense, triangular atom nets), while the cation layers contain ‘vacancies,’ which are necessary to accommodate the cation deficiency (compared with anion concentration) in both compounds (these ‘vacancies’ actually are interstices; they are ‘holes’ in the otherwise fully dense triangular atom nets 127 that make up each cation layer) Table shows the arrangement of cation and anion layers in spinel and alumina, along h111i and [0001] directions, respectively.11 Both structures can be described by a 24-layer stacking sequence along these directions Both spinel and alumina can be thought of as consisting of pseudo-close-packed anion sublattices, with cation layers interleaved between the anion layers The anion sublattice in spinel is cubic close-packed (ccp) with an ABCABC layer stacking arrangement, while alumina’s anion sublattice is hexagonal closepacked (hcp) with BCBCBC layer stacking In both structures, between each pair of anion layers there are three layers of interstices where cations may reside: a tetrahedral (t) interstice layer, followed by an octahedral (o) interstice layer, followed by another t layer In spinel, Mg cations reside on t layers, while Al cations occupy the o layers In alumina, all t layers are empty and Al occupies 2/3 of the o layer interstices In spinel, cation interlayers alternate between a pure Al kagome´ layer and a mixed MgAlMg, threelayer thick slab In alumina, each interlayer is pure Al in a honeycomb arrangement 1.05.2.3.2 Charge on interstitial dislocations In addition to spinel and alumina layer stacking sequences, Table also shows the layer ‘blocks’ that have been found to comprise {111} and (0001) interstitial dislocation loops in spinel and alumina, respectively An interstitial loop in spinel is composed of four layers such that the magnitude of the Burgers vector, b, along h111i is 1/6 h111i The composition of each of these blocks has stoichiometry M3O4, where M represents a cation (either Mg or Al) and O is an oxygen anion The upper 1/6 h111i block in Table has an actual composition of Al3O4, while the lower 1/6 h111i block has a composition of Mg2AlO4 If Mg and Al cations assume their formal valences (2ỵ and 3ỵ, respectively), and O anions are 2, then the blocks described here are charged: (Al3O4)1ỵand (Mg2AlO4)1 This may result in an untenable situation of excess Coulombic energy, as each molecular unit in the block possesses an electrostatic charge of esu It has been proposed that this charge imbalance is overcome by partial inversion of the cation layers in the 1/6 h111i blocks.12 (Inversion in spinel refers to exchanging Mg and Al lattice positions such that some Mg cations reside on o sites, while a similar number of Al cations move to t sites.) If a random cation distribution is inserted into either the upper or lower 1/6 h111i block shown in Table 1, then the block becomes charge neutral, that is, (MgAl2O4)x 128 Layer # 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Layer stacking of {111} planes along h111i in cubic spinel and (0001) planes along [0001] in hexagonal alumina Layer height 23/24 22/24 (11/12) 21/24 (7/8) 20/24 (5/6) 19/24 18/24 (3/4) 17/24 16/24 (2/3) 15/24 (5/8) 14/24 (7/12) 13/24 12/24 (1/2) 11/24 10/24 (5/12) 9/24 8/24 (1/3) 7/24 6/24 (1/4) 5/24 4/24 (1/6) 3/24 (1/8) 2/24 (1/12) 1/24 0/24 –1/24 Spinel (MgAl2O4) {111}-layer stacking along h111i direction Alumina (a-Al2O3) (0001)-layer stacking along [0001] direction O ¼ oxygen t ¼ tetrahedral interstices o ¼ octahedral interstices Layer registry (ABCABC-type O-stacking) Layer composition O ¼ oxygen t ¼ tetrahedral interstices o ¼ octahedral interstices t O t o t O t o t O t o t O t o t O t o t O t o t C B A C B A C B A C B A C B A C B A C B A C B A C – O4 Mg1 Al1 Mg1 O4 – Al3 – O4 Mg1 Al1 Mg1 O4 – Al3 – O4 Mg1 Al1 Mg1 O4 – Al3 – Frank loop Burgers vectors 1/6 ẳ layers (Al3O4)1ỵ 1/6 ẳ layers (Mg2AlO4)1À t O t o t O t o t O t o t O t o t O t o t O t o t Layer registry (BCBC-type O-stacking) C a3 B a2 C a1 B a3 C a2 B a1 Layer composition – O3 – Al2 – O3 – Al2 – O3 – Al2 – O3 – Al2 – O3 – Al2 – O3 – Al2 – Frank loop Burgers vectors 1/3 [0001] ¼ layers (excluding empty tetrahedral layers) (Al2O3)x Radiation-Induced Effects on Material Properties of Ceramics Table Radiation-Induced Effects on Material Properties of Ceramics 129 Table indicates that an (0001) interstitial dislocation loop in alumina consists of a four-layer block (excluding the empty t layers) such that the magnitude of the Burgers vector, b, along [0001] is 1/3 [0001] The composition of each of these blocks is Al2O3, which is charge neutral, that is, (Al2O3)x Thus, there are no Coulombic charge issues associated with interstitial dislocation loops along in alumina These dislocation loops consist simply of a pair of Al layers interleaved with two O layers specifically at the position of the red vertical line in the last sequence Kronberg13 refers to this as an unsymmetrical electrostatic fault This fault is seen to be intrinsic and only in the cation sublattice; the anion sublattice is undisturbed In summary, the dislocation loop formed by 1/3 [0001] block insertion in alumina is an intrinsic, cation-faulted, interstitial Frank loop This is also a sessile loop 1.05.2.3.3 Lattice registry and stacking faults I: (0001) Al2O3 Now, we consider the formation of an interstitial dislocation loop along in spinel In spinel, O anion layers are fully dense triangular atom nets stacked in a ccp, ABCABC geometry (A, B, and C are all distinct layer registries) Between adjacent O layers, 3/4 dense Al and MgAlMg layers are inserted, with registries labeled a, b, and c in Table (a cations have the same registry as A anions; likewise, b same as B, c same as C) For stacking fault layer stacking assessments in spinel, it is conventional to simplify the layer notation for the cations (see, e.g., Clinard et al.6) The successive kagome´ Al layers are labeled a, b, g, while the MgAlMg mixed atom slabs are each projected onto one layer and labeled a0 , b0 , g0 With these definitions, the registry of cation/anion stacking in spinel follows the sequence: a C b0 A g B a0 C b A g0 B As with alumina, when extra pairs of cation and anion layers are inserted into the spinel stacking sequence, a C b0 A g B a0 C b A g0 B, a fault in the stacking sequence is introduced One can demonstrate how this works by inserting a 1/6 h111i b A block into the stacking sequence described above (this is equivalent to the upper Burgers vector for spinel shown in Table 1, which uses a kagome´ Al cation layer) We obtain: Next, we must consider the lattice registry of the layer blocks inserted into alumina and spinel to form interstitial dislocation loops along Registry refers to the relative translational displacements between successive layers in a stack In alumina, O anion layers are fully dense triangular atom nets, stacked in an hcp, BCBCBC geometry B and C represent two distinct layer registries (displaced laterally with respect to one another) All the Al cation layers occur within the same registry, labeled a in Table (a is displaced laterally relative to B and C) These Al layers are 2/3 dense, relative to the fully dense O layers, forming honeycomb atomic patterns The successive Al layers are differentiated by where the cation ‘vacancies’ occur within each a layer There are three possibilities that occur sequentially, hence the subscripted labels in Table (a1, a2, a3).11 Thus, the registry of cation/anion stacking in alumina follows the sequence: a1 B a2 C a3 B a1 C a2 B a3 C When extra pairs of Al and O layers are inserted into the stacking sequence, a1 B a2 C a3 B a1 C a2 B a3 C, a mistake in the stacking sequence is introduced In other words, the dislocation loop formed by the block insertion is faulted (contains a stacking fault) Let us see how this works by inserting a 1/3 [0001] four-layer block, Al2ÁO3ÁAl2ÁO3, into the stacking sequence described above We obtain: ðbeforeÞ a C b0 A g B a0 C b A g0 B b A a C b0 A g B b0 A g B a0 C b A g0 B ðafter; showing stacking fault positionsÞ a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a1 B a2 C a3 B a1 C a2 B a3 C ðafterÞ a1 a2 a3 a1 a2 a3 a1 a2 j a1 a2 a3 a1 a2 a3 ðafter; showing only cations and showing stacking fault positionÞ a C b A g B a0 C b A g B a C b A g B a0 C b A g0 B ðbeforeÞ a0 C b A g0 B ðafterÞ a C b A g B a0 C b A g B j b A j a C a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B a1 C a2 B a3 C 1.05.2.3.4 Lattice registry and stacking faults II: {111} MgAl2O4 ½2Š Notice in eqn [2] that after block insertion, the anion sublattice is not faulted (BCBC layer stacking is preserved), whereas the cation sublattice is faulted, ½3Š Notice in eqn [3] that after block insertion, both the anion sublattice (CABCAB stacking is not preserved) and the cation sublattice are faulted Also, notice that the cation and anion stacking sequences are faulted on both sides of the inserted b A block (the layer sequences are broken approaching the block from both the left and the right) Thus, 130 Radiation-Induced Effects on Material Properties of Ceramics the b A block actually contains two stacking faults, on either side of the block The positions of these stacking faults are denoted by vertical red lines in eqn [3] The dislocation loop formed by 1/6 h111i block insertion in spinel is an extrinsic, cationỵanion faulted, sessile interstitial Frank loop We can also consider inserting a 1/6 h111i b0 A block into the spinel stacking sequence (i.e., the lower spinel Burgers vector shown in Table 1, which uses a mixed MgAlMg cation slab) We obtain: a C b0 A g B a0 C b A g0 B a C b0 A g B a0 C ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ðbeforeÞ ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ ða2 CÞ b A g0 B ðbeforeÞ a C b0 A g B a0 C b A g0 B b0 A a C b0 A g B ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ðafterÞ ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ ða2 CÞ j a0 C b A g0 B ðafterÞ a C b A g B a C b A g B j b0 A j a C b0 A g B a0 C b A g0 B ðafter; showing stacking fault positionsÞ anion and cations together, we can write the {1010} stacking sequence in alumina as (a1B) (a2C) (a3B) (a1C) (a2B) (a3C) Now, as with the basal plane story described earlier, when an extra 1=3h1010i two-layer block, (Al2O3)xÁ(Al2O3)x, is inserted into the stacking sequence, (a1B) (a2C) (a3B) (a1C) (a2B) (a3C), a stacking fault occurs as follows: ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ðafter; showing stacking fault positionị ẵ4 Once again, both the anion and cation sublattices are faulted, and we obtain an extrinsic, cationỵanion faulted, sessile interstitial Frank loop 1.05.2.3.5 Lattice registry and stacking faults III: {1010} Al2O3 So far we have considered Coulombic charge and faulting for 1/3 [0001] (0001) loops in alumina and 1/6 h111i {111} loops in spinel Now, we must repeat these considerations for 1=3h1011if1010g prismatic loops in alumina and 1/4 h110i {110} loops in spinel We begin with alumina prismatic loops Alumina {1010} prism planes contain both Al and O in the ratio 2:3, that is, identical to the Al2O3 compound stoichiometry Along the h1010i direction normal to the traces of the {1010} planes, the registry of the {1010} planes varies between adjacent planes, analogous to the registry shifts that occur between adjacent (0001) basal planes in alumina (discussed earlier) However, the patterns of Al atoms in all {1010} planes are identical Similarly, the O atom patterns are identical in all {1010} planes The registry of the O atom patterns between adjacent {1010} planes alternates every other layer, analogous to the BCBC stacking of oxygen basal planes (Table 1, eqns [2–4]) On the other hand, the registry of the Al cation patterns is distinct from the O pattern registries (B and C), and the registry of the Al patterns only repeats every fourth layer In other words, the stacking sequence of {1010} plane Al atom patterns can be described using the same nomenclature as in Table and eqn [2] for (0001) alumina planes, that is, a1 a2 a3 a1 a2 a3 Putting the ½5Š Notice in eqn [5] that after block insertion, the anion sublattice is not faulted (BCBC layer stacking is preserved), whereas the cation sublattice is faulted, specifically at the position of the red vertical line in the last sequence Similar to the case of basal plane interstitial loop formation in alumina (discussed earlier), the dislocation loop formed by 1=3h1010i block insertion in alumina is an intrinsic, cation-faulted, sessile interstitial Frank loop 1.05.2.3.6 Lattice registry and stacking faults IV: {110} MgAl2O4 Next, we consider 1/4 h110i {110} loops in spinel Spinel {110} planes alternate in composition, (AlO2)(MgAlO2)ỵ ., such that each layer is a mixed cation/anion layer To insert a charge-neutral interstitial slab along h110i in spinel requires that we insert a {110} double-layer block, (AlO2)(MgAlO2)ỵ, that is, a stoichiometric MgAl2O4 unit The thickness of this slab is a/4 h110i, where a is the spinel cubic lattice parameter Along the h110i direction normal to the traces of the {110} planes, the registry of the {110} planes varies between adjacent planes, analogous to the registry shifts that occur between adjacent {111} planes in spinel (discussed earlier) The O atom patterns are identical in all {110} planes, but the registry of the O atom patterns between adjacent {110} planes alternates every other layer, analogous to the BCBC stacking described earlier The Mg atom patterns are identical in each (MgAlO2)ỵ layer, while the registry of the Mg atom patterns alternates every other (MgAlO2)ỵ layer We denote the Mg stacking sequence by a1 a2 a1 a2 There are two Al atom patterns along h110i: (1) the first Radiation-Induced Effects on Material Properties of Ceramics occurs in each (AlO2)À layer with no change in registry between layers (we denote this Al pattern by b0 ); and (2) the second occurs in each (MgAlO2)ỵ layer, and the registry of these Al atom patterns alternates every other (MgAlO2)ỵ layer (we denote this Al stacking sequence by b1 b2 b1 b2 ) Combining all these considerations, we can write the {110} planar stacking sequence in spinel as follows: (b0 B) (a1b1C) (b0 B) (a2b2C) Now, as with the spinel {111} case described earlier, when an extra 1/4 h110i two-layer block, (AlO2)(MgAlO2)ỵ, is inserted into the spinel {110} stacking sequence, (b0 B) (a1b1C) (b0 B) (a2b2C), a stacking fault occurs as follows: c c 500 nm ðb0 BÞ ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ ðb0 BÞ ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ ðbeforeÞ 0 ðb BÞ ða1 b1 CÞ ðb BÞ ða2 b2 CÞ ðb BÞ ða1 b1 CÞ ðb0 BÞ ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ 0 ðafterÞ ðb BÞ ða1 b1 CÞ ðb BÞ ða2 b2 CÞ ðb BÞ ða1 b1 CÞ j ðb0 BÞ j ða1 b1 CÞ ðb0 BÞ ða2 b2 Cị after; showing stacking fault positionsị 131 ẵ6 Notice in eqn [6] that after block insertion, the anion sublattice is not faulted (BCBC layer stacking is preserved), whereas the cation sublattice is faulted, specifically at the positions of the red vertical lines in the last sequence (the left-hand red line corresponds to the cation fault position for cation planar registries moving from right to left; likewise, the right-hand red line corresponds to the cation fault position for cation planar registries moving from left to right) Thus, the dislocation loop formed by 1/4 h110i twolayer block insertion in spinel is an extrinsic, cationfaulted, sessile interstitial Frank loop Figure shows an example of 1/4 h110i interstitial dislocation loops in spinel, produced by neutron irradiation.12 The alternating black-white fringe contrast within the loops is an indication of the presence of a stacking fault within the perimeter of each loop The character of the {110} loops was determined by Hobbs and Clinard using the TEM imaging methods of Groves and Kelly,14,15 with attention to the precautions outlined by Maher and Eyre.16 These loops were determined to be extrinsic, faulted 1/4 h110i {110} interstitial dislocation loops It is evident in Figure that the extrinsic fault associated with these loops is not removed by internal shear, even when the loops grow to significant sizes (>1 mm diameter) This is the subject of our next topic of discussion, namely, the unfaulting of faulted Frank loops Figure Bright-field transmission electron microscopy (TEM) image of {110} faulted interstitial loops in MgAl2O4 single crystal irradiated at 1100 K to a fluence of 1.9  1026 n mÀ2 ($20 dpa) Reproduced from Hobbs, L W.; Clinard, F W., Jr J Phys 1980, 41(7), C6–232–236 The surface normal to the TEM foil is along h111i The dislocation loops intersect the top and bottom surfaces of the TEM foil, which gives them their ‘trapezoidal’ shapes The areas marked ‘C’ in the micrograph are regions where a ‘double-layer’ loop has formed, that is, a second Frank loop has condensed on planes adjacent to the preexisting faulted loop 1.05.2.3.7 Unfaulting of faulted Frank loops I: (0001) Al2O3 In principle, faulted interstitial Frank loops can unfault by dislocation shear reactions This should occur at a critical stage in interstitial loop growth, when the energy of the faulted dislocation loop, with a relatively small Burgers vector, becomes equal to an equivalently sized, unfaulted dislocation loop, with a larger Burgers vector (In the absence of a stacking fault, the energy of a dislocation scales as b2, where b is the magnitude of the Burgers vector.) From this critical point on, the energy cost to incrementally grow the size of a dislocation loop favors the unfaulted loop, since there is no cost in energy due to a stacking fault within the loop perimeter We examine first the unfaulting of 1/3 [0001] (0001) loops in alumina To unfault a 1/3 [0001] (0001) dislocation loop in alumina, we must propagate a 1=3½1010Š partial shear dislocation across the loop plane.6 This is described by the following dislocation reaction: 3ẵ0001 ỵ 13ẵ1010 ! 3ẵ1011 faulted loop partial shear unfaulted loop basalị ẵ7 132 Radiation-Induced Effects on Material Properties of Ceramics After propagating the partial shear through the loop, we are left with an unfaulted layer stacking sequence The Burgers vector of the resultant dislocation loop, 1=3½1011Š, is a perfect lattice vector; therefore, the newly formed dislocation is a perfect dislocation The resultant 1=3½1011Š (0001) dislocation is a mixed dislocation, in the sense that the Burgers vector is canted (not normal) relative to the plane of the loop 1.05.2.3.8 Unfaulting of faulted Frank loops II: {111} MgAl2O4 C 1/3 [1011] 1/3 [0001] 1/3 [1010] Figure Alumina cation ‘honeycomb’ atom nets along the c-axis in Al2O3 corundum (anion sublattice not shown here) The black circles represent Al atoms The gray squares represent cation ‘vacancies.’ The diagram shows the Burgers vectors involved in the partial shear unfaulting reactions for interstitial dislocation loops in alumina Adapted from Howitt, D G.; Mitchell, T E Philos Mag A 1981, 44(1), 229–238 This reaction is shown graphically in Figure Note that the magnitude of 1=3½1010Š is approximately the Al–Al (and O–O) first nearest-neighbor spacing in Al2O3 When we pass a 1=3½1010Š shear through a 1/3 [0001] (0001) dislocation loop, the cation planes beneath the loop assume new registries such that in eqn [2], a1, a2, and a3 commute as follows: a1 ! a3 ! a2 ! a1 The anion layers beneath the loop are left unchanged (B ! B, C ! C) Taking the faulted (0001) stacking sequence in eqn [2] and assuming that the planes to the right are above the ones on the left, we perform the 1=3½1010Š partial shear operation as follows: a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 |C a1 B a2 C a3 B a1 C a2 B a3 C (faulted) C a3 B a1 C a2 B a3 C a1 B a2 C a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C (unfaulted) [8] For this particular dislocation loop, it is thought that rather than unfaulting, 1/6 h111i {111} dislocations simply dissolve back into the lattice, in favor of the more stable 1/4 h110i {110} loops.12 As discussed earlier, the 1/6 h111i {111} dislocation can be presumed to be relatively unstable because it possesses both anion and cation faults, and in addition, it cannot preserve stoichiometry or charge balance in either normal or inverse spinel.12 Counter to this argument is the idea that if a 1/6 h111i {111} dislocation loop incorporates a partial inversion of its cation content, then this loop could be made both stoichiometric and charge neutral Such a dislocation would arguably be more stable However, {111} loops are never observed to grow very large ( 0.18 MeV) ($2.4 dpa) Yano and Iseki36 found the same loops in b-SiC irradiated at 640  C to 1.0  1023 n cmÀ2 (E > 0.10 MeV) ($100 dpa) and, using high-resolution TEM, determined these to be 1/3 h111i {111} interstitial Frank loops These loops are constructed by inserting a single extra Si-C layer into the CABCAB Si-C stacking sequence This produces the sequence CAjC B jCAB, where the prime denotes a p rotation of the tetrahedral unit (note that an adjacent Si-C layer is modified by the insertion of the extra Si-C layer) In 6H-type hexagonal a-SiC, Yano and Iseki36 found ‘black spot’ defects lying on (0001) planes following neutron irradiation at 840  C to 1.7  1021 n cmÀ2 (E > 0.10 MeV) ($1.7 dpa) They coarsened these defects using high-temperature annealing and determined the defects to be interstitial Frank loops The stacking sequence along (0001) in 6H a-SiC is ABCA B C Yano and Iseki proposed that the Frank loops are formed by a mechanism similar to b-SiC (described above), wherein insertion of an extra Si-C layer modifies an adjacent Si-C layer to produce a sequence such as ABCjB 0A jC B Such a defect is described as a 1/6 [0001] (0001) interstitial Frank loop For low temperatures (150–800  C), small amounts of swelling (0–2%) are observed in monolithic SiC samples produced by chemical vapor deposition (CVD).33 It should be noted that CVD-SiC is cubic and highly faulted.37 This swelling saturates at low damage levels (a few dpa) and the saturated swelling is lower, the higher the temperature Much of this swelling is due to strain caused by surviving interstitials formed during ballistic damage cascades As the irradiation temperature approaches 1000  C, the surviving defect fraction diminishes because interstitial mobility increases with temperature and i–v recombination is enhanced Newsome et al.33 found swelling values of 1.9, 1.1, and 0.7% for neutron irradiations at 300, 500, and 800  C, respectively Above 1000  C, neutron irradiation-induced void formation in b-SiC was first observed by Price35 at 1250  C (4.3–7.4 dpa) and 1500  C (5.2–8.8 dpa) Interestingly, no dislocation loops were observable by TEM in these samples Price35 postulated that 137 the interstitials may have been annihilated at stacking faults Alternatively, he suggested that interstitial defects were present following irradiation, but they were too small and the contrast too weak to detect them Nevertheless, at present it is not clear whether void formation in SiC is due to vacancy supersaturation produced by a dislocation bias In any case, swelling of a few percent was observed for irradiations at temperatures greater than 1000  C, and Price38 speculated that this swelling probably does not saturate with dose At low temperatures ($60  C), Snead and Hay37 observed both a- and b-SiC to amorphize following a total fast neutron fluence of 2.6  1021 n cmÀ2 ($2.6 dpa) This amorphization transformation was accompanied by a large reduction in density ($10.8%), that is, volumetric swelling of nearly 11% Snead and Hay37 estimated that the critical temperature for amorphization (the temperature above which amorphization is not possible) is $125  C (a lower limit for the threshold amorphization temperature) The critical temperature is dose rate dependent In the study above, the dose rate was $8  10–7 dpa sÀ1 In other electron and ion irradiation experiments with dose rates of $1  10–3 dpa sÀ1, researchers found critical temperatures ranging from 20 to 70  C for MeV electron irradiations,39–41 $150  C for energetic Si ions,42 and $220  C for 1.5 MeV Xe ions.43,44 1.05.3.3 Radiation Effects in Graphite Graphite (C) is a very important material for nuclear energy applications Graphite is a moderator used to thermalize neutrons in thermal gas and water-cooled reactors in the United Kingdom and the Soviet Union, respectively.45 Pyrolitic graphite is one of the barrier coating materials used in TRISO coated fuel particles.33 Graphite and carbon composites are also used as plasma-facing materials in fusion reactors.46 Numerous radiation effects studies have been performed on graphite Nevertheless, the behavior of graphite in a radiation damage environment remains poorly understood This is due primarily to the fact that graphite comes in so many forms and is produced in so many different ways, that in fact, the structure and chemistry of graphite used in nuclear applications is not a well-defined constant Nevertheless, there are some aspects of the crystal structure of graphite and the changes in this structure induced by irradiation that are somewhat analogous to the discussion of Al2O3 versus MgAl2O4, presented earlier in this chapter 138 Radiation-Induced Effects on Material Properties of Ceramics Graphite is a hexagonal crystalline material, with an ABAB layer stacking arrangement of carbon sheets These carbon layers have obvious hexagonal atom patterns in them However, they are not fully dense triangular atom nets, as would be the case in a close-packed structure They are so-called graphene sheets, in which the atom pattern is a honeycomb pattern, identical to the cation layer patterns in Al2O3 (see Section 1.05.2.3.1) Each C atom is surrounded by three nearest-neighbor C atoms, and the bonding linking each C atom with its neighbors is characterized by sp2 hybridization The bonding that links adjacent graphene layers is weak, Van der Waals-type bonding The interstitial dislocation loops that form in irradiated graphite, by the condensation of freely migrating interstitial point defects, form (not surprisingly) on (0001) basal planes, between adjacent graphene layers In some of the earliest work on radiation effects in graphite, this was described as follows47: When subjected to bombardment with fission neutrons, primary collisions displace carbon atoms from their normal sites in the layers, driving them to sites between planes (interstitial or interlamellar positions) This loop nucleation is analogous to the (0001) basal interstitial loops that form in Al2O3 during the initial stages of irradiation (Section 1.05.2.3.1) However, the basal loops in graphite not grow to any significant size Instead, the graphene layers adjacent to interlamellar loop nuclei buckle, which causes a net increase in the c-dimension of the hexagonal material and a concomitant decrease in the a-dimension.48 This buckling is believed to be due to sp3 bond formation between C interstitials and C atoms in the graphene planes.49,50 The overall macroscopic effect of c-axis expansion and a-axis shrinkage is dimensional changes of crystallites within the graphite Macroscopic radiation damage effects in graphite are discussed in detail in Chapter 4.10, Radiation Effects in Graphite 1.05.3.4 Radiation Effects in Other Ceramics Numerous additional ceramics have been either used or proposed for nuclear reactor materials applications These include graphite (discussed in other chapters in this volume) as well as carbides and nitrides, such as ZrC and ZrN, which have higher thermal conductivities than their sister oxide compound, ZrO2 Research into the radiation damage properties of these materials is in its infancy, and therefore, these compounds are not described in further detail here 1.05.4 Summary The response of ceramic materials to radiation is especially complex because ceramics (with the exception of graphite) are made up of anions and cations (sometimes several different cations) such that the atomic defects that initiate radiation damage are different in their size, chemistry, charge, mobility, and so on Thus, it is difficult to predict how the microstructure of a ceramic will evolve under irradiation and, in turn, how properties such as structural stability will change in response to the radiation-induced microstructural alterations Nevertheless, we present a case study (described below) wherein researchers have succeeded in explaining the extraordinary differences between the radiation responses of two important engineering ceramics We devoted much of this chapter to comparing and contrasting the high-temperature radiation damage response of two quite similar refractory, dielectric ceramics: a-alumina (Al2O3) and magnesio-aluminate spinel (MgAl2O4) Al2O3 is highly susceptible to radiation-induced swelling, whereas MgAl2O4 is not The swelling of Al2O3 is due to excessive void formation in the crystal lattice We considered in detail in this chapter the atomic and microstructural mechanisms that help to explain why voids nucleate and grow in Al2O3 to a very significant degree, whereas in MgAl2O4, this problem is much less pronounced We showed that the reasons for the great differences between the radiation damage behavior of Al2O3 and MgAl2O4 have mainly to with differences in the way interstitial loops nucleate and grow in these two oxides The hope is that by understanding these differences, we will by analogy be able to understand the radiation damage behavior of other ceramic materials In this chapter, we also examined two different phenomena that lead to degradation in the mechanical properties of ceramics: (1) nucleation and growth of interstitial dislocation loops and voids and (2) crystal-to-amorphous phase transformations Both these phenomena cause macroscopic swelling of materials This ultimately leads to the failure of materials because of unacceptable dimensional changes, microcracking, excessive increases in hardness (or alternatively, softening in the case of amorphization), and so on Radiation-Induced Effects on Material Properties of Ceramics We concluded this chapter with brief discussions of a few ceramics additionally important for nuclear energy applications, namely silicon carbide (SiC), uranium dioxide (UO2), and graphite (C) 25 26 27 28 References 10 11 12 13 14 15 16 17 18 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that this sequence ends in an unfaulted, perfect interstitial loop This final loop configuration should be... charge and faulting for 1/ 3 [00 01] (00 01) loops in alumina and 1/ 6 h 111 i {11 1} loops in spinel Now, we must repeat these considerations for 1= 3h1 011 if1 010 g prismatic loops in alumina and 1/ 4 h 110 i